Iterative paraxial tracing-based model for solving the aberration field decenter vector in aberration analysis

Aberration analysis helps to understand the potential relationship between optical imaging system parameters and aberrations, thereby providing guidance for improving system performance. Nodal aberration theory plays a vital role in the aberration analysis of rotationally asymmetric systems. This theory establishes an analytic connection between the system aberration field and parameters of the misaligned optical elements, through a key factor known as the aberration field decenter vector (AFDV). However, the available system structures with a definite analytic expression of AFDV are quite limited. In this paper, a detailed solving model of AFDV is proposed. This model supports the calculation of AFDV for reflective systems with arbitrary structures. The AFDV calculation formulas of the design examples are obtained, with the relative calculation error of 0.63%. By applying the AFDV formulas to aberration analysis, the aberration nodes of example systems are correctly predicted. In addition, an aberration-based alignment method for the misaligned coaxial four-mirror system is established, resulting in a recovery of over 98% in system performance after the first alignment. We believe this research has significant implications for optical system design, desensitization, and alignment.